Nucleus-nucleus potential with shell-correction contribution

The full relaxed-density potential between spherical nuclei is considered as a sum of the macroscopic and shell-correction contributions. The macroscopic part of the potential is related to a nucleus-nucleus potential obtained in the framework of the extended Thomas-Fermi approach with the Skyrme and Coulomb forces and the relaxed-density ansatz for evaluation of proton and neutron densities of interacting nuclei. A simple prescription for the shell-correction part of the total potential is discussed. The parameters of the shell-correction and macroscopic parts of the relaxed-density potential are found by fitting the empirical barrier heights of the 89 nucleus-nucleus systems as well as macroscopic potentials evaluated for 1485 nucleus-nucleus systems at 12 distances around touching points.

Figure 1

Absolute differences between 89 empirical barrier heights [36, 45, 46, 47] and barrier heights evaluated using the relaxed density with the shell-correction contribution (relax), frozen-density (frozen) [35], Krappe-Nix-Sirk (KNS) [31], Bass (Bass80) [1], Bass (Bass74) [27], proximity (Prox77) [30], proximity (Prox2000) [34], Winter [33], and Siwek-Wilczynska-Wilczynski (SWW) [10] potentials.

Figure 2

Relative differences between 89 empirical barrier heights and barrier heights evaluated with the help of various potentials. The notations are the same as in Fig. 1.

Figure 3

Nucleus-nucleus potentials for the system ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ evaluated with the help of various approaches. The empirical value of the barrier height is shown by a horizontal arrow and the touching distance of these nuclei by a vertical arrow.

Figure 4

Full relaxed-density potential with the shell-correction contribution for the system ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ evaluated for various contributions of the shell-correction energies to the potential.